A micro-electro-mechanical system, MEMS, microphone assembly comprises an enclosure (10) defining a first cavity (11), and a MEMS microphone (20) arranged inside the first cavity (11). The microphone (20) comprises a first die (21) with bonding structures (23) and a MEMS diaphragm (24), and a second die (22) having an application specific integrated circuit, ASIC. The second die (22) is bonded to the bonding structures (23) such that a gap (28) is formed between a first side (25) of the diaphragm (24) and the second die (22), with the gap (28) defining a second cavity (31). The first side (25) of the diaphragm (24) is interfacing with the second cavity (31) and a second side (26) of the diaphragm (24) is interfacing with the environment (2) via an acoustic inlet port (12) of the enclosure (10). The bonding structures (23) are arranged such that pressure ventilation openings (30) are formed that connect the first cavity (11) and the second cavity (31).